Nonminimally coupled curvature-matter gravity models and Solar System constraints

TL;DR

This paper investigates nonminimally coupled curvature-matter gravity models, assessing their compatibility with Solar System experiments, and finds that certain models can explain cosmic acceleration while remaining consistent with local gravitational tests.

Contribution

It introduces and analyzes a nonminimally coupled gravity model extending $1/R^n$ gravity, demonstrating its viability and deriving constraints from Solar System observations.

Findings

The NMC model can predict cosmic acceleration.

It remains compatible with Solar System tests unlike $f(R)=1/R^n$ models.

Constraints on model parameters are derived from Mercury's perihelion precession.

Abstract

We discuss constraints to some nonminimally (NMC) coupled curvature-matter models of gravity by means of Solar System experiments. First we discuss a NMC gravity model which constitutes a natural extension of $1/R^n$ gravity to the nonminimally coupled case. Such a NMC gravity model is able to predict the observed accelerated expansion of the Universe. Differently from the $f(R)=1/R^n$ gravity case, which is not compatible with Solar System observations, it turns out that this NMC model is a viable theory of gravity. Then we consider a further NMC gravity model which admits Minkowski spacetime as a background, and we derive the $1/c$ expansion of the metric. The nonrelativistic limit of the model is not Newtonian, but contains a Yukawa correction. We look for trajectories around a static, spherically symmetric body. Since in NMC gravity the energy-momentum tensor of matter is not conserved, then the trajectories deviate from geodesics. We use the NMC gravity model to compute the perihelion precession of planets and we constrain the parameters of the model from radar observations of Mercury.